The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62 minutes and a standard deviation of 18 minutes. Suppose one person at the hot springs is

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A normal distribution problem 

The amount of time that people spend at
Grover Hot Springs is normally
distributed with a mean of 62 minutes
and a standard deviation of 18 minutes.
Suppose one person at the hot springs is
randomly chosen. Let X = the amount of
time that person spent at Grover Hot
Springs . Round all answers to 4 decimal
places where possible.
a. What is the distribution of X? X ~ N(
b. Find the probability that a randomly
selected person at the hot springs stays
longer then 75 minutes.
c. The park service is considering
offering a discount for the 4% of their
patrons who spend the least time at the
hot springs. What is the longest amount
of time a patron can spend at the hot
springs and still receive the discount?
minutes.
Transcribed Image Text:The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62 minutes and a standard deviation of 18 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( b. Find the probability that a randomly selected person at the hot springs stays longer then 75 minutes. c. The park service is considering offering a discount for the 4% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes.
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